## phân tích đa thức thành nhân tử: a) $x^{2}$ $y^{2}$ + 1 – $x^{2}$ – $y^{2}$ b) $x^{4}$ – $x^{2}$ + 2x – 1 c) 3a – 3b + $a^{2}$ – 2ab + $b^{2}$ d)

Question

phân tích đa thức thành nhân tử:
a) $x^{2}$ $y^{2}$ + 1 – $x^{2}$ – $y^{2}$
b) $x^{4}$ – $x^{2}$ + 2x – 1
c) 3a – 3b + $a^{2}$ – 2ab + $b^{2}$
d) $a^{2}$ + 2ab + $b^{2}$ – 2a – 2b + 1
e) $a^{2}$ – $b^{2}$ – 4a + 4b
f) ( $a^{2}$ + $b^{2}$ + ab ) ^2 – a^2b^2 – b^2c^2 – c^2a^2
g) 4$a^{2}$ $b^{2}$ – ( $a^{2}$ + $b^{2}$ – 1 ) ^2
h) ( xy + 4 ) ^2 – ( 2x + 2y ) ^2

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8 months 2020-11-24T17:59:37+00:00 1 Answers 66 views 0

1. Giải thích các bước giải

a)
$x^2.y^2+1-x^2-y^2=x^2(y^2-1)-(y^2-1)=(x^2-1)(y^2-1)$
$=(x-1)(x+1)(y+1)(y-1)$
b)

$x^4-x^2+2x-1=x^4-(x-1)^2=(x^2-x+1)(x^2+x-1)$
c)
$3a-3b+a^2-2ab+b^2=3(a-b)+(a-b)^2=(a-b)(a-b+3)$
d)
$a^2+2ab+b^2-2a-2b+1=(a+b-1)^2$
e)
$a^2-b^2-4a+4b=(a-b)(a+b)-4(a-b)=(a-b)(a+b-4)$
f)
$(a^2+b^2+ab)^2-a^2b^2-b^2c^2-c^2a^2$
$=(a^2+b^2)(a^2+b^2+2ab)-c^2(a^2+b^2)$
$=(a^2+b^2)((a+b)^2-c^2)$
$=(a^2+b^2)(a+b+c)(a+b-c)$
g)$4a^2b^2-(a^2+b^2-1)^2$
$=(2ab-a^2-b^2+1)(2ab+a^2+b^2-1)$
$=(1-(a-b)^2)((a+b)^2-1)$
$=(1-a+b)(1+a-b)(a+b-1)(a+b+1)$
h)
$(xy+4)^2-(2x+2y)^2$
$=(xy-2x-2y+4)(xy+2x+2y+4)$
$=(x-2)(y-2)(x+2)(y+2)$